[Bob W]

Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from dubbing
some my favorite LP's to DAT several years ago. These files are now on the
computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a dithering
algorithm before burning to audio CD's?

Thanks in advance,

Bob W



__________ Information from ESET Smart Security, version of virus signature database 4087 (20090519) __________

The message was checked by ESET Smart Security.

http://www.eset.com

[Don Pearce[_3_]]

On Tue, 19 May 2009 09:37:28 -0500, "Bob W" wrote:

Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from dubbing
some my favorite LP's to DAT several years ago. These files are now on the
computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a dithering
algorithm before burning to audio CD's?

Thanks in advance,

No. The DAT did that for you, and also you can't dither after the fact
- it has to be applied before digitisation, or you get both noise and
quantization distortion.

d

[Scott Dorsey]

Bob W wrote:
Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from dubbing
some my favorite LP's to DAT several years ago. These files are now on the
computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a dithering
algorithm before burning to audio CD's?

No. Why would you want to? You're not changing the word length or
altering the levels or anything. You have 16 bit wave files from a
16 bit source, right?
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Paul Stamler[_2_]]

"Bob W" wrote in message
...
Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from dubbing
some my favorite LP's to DAT several years ago. These files are now on
the computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a dithering
algorithm before burning to audio CD's?

Only if you're processing them in any way (level changes, etc.), in which
case you should convert to 24 bit or 32 bit, do the changes, then dither
back to 16 bits. If not, leave them alone.

Peace,
Paul

[Geoff]

Bob W wrote:
Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from
dubbing some my favorite LP's to DAT several years ago. These files are
now
on the computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a
dithering algorithm before burning to audio CD's?

Only if you change them in some way. But check that the process you are
doing does inherently include dither in the first place.

geoff

[WillStG]

On May 19, 11:16 am, (Scott Dorsey) wrote:
Bob W wrote:
Hi, I have a number of DAT tapes (16 bit/44.1kHz) resulting from dubbing
some my favorite LP's to DAT several years ago. These files are now on the
computer as wave files and I intended to burn them onto audio CD's.
(Redbook)

Would it be best to run these 16bit / 44.1kHz files through a dithering
algorithm before burning to audio CD's?

No. Why would you want to? You're not changing the word length or
altering the levels or anything. You have 16 bit wave files from a
16 bit source, right?
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Well you do have the option to apply dither when you burn CDs
using Toast. But I think the dither option is intended for when you
are applying fade in and fade outs, or using the AU plug ins options.
Why one would wish to burn Redbook CD's of one's record collection
though, I dunno. Redbook isn't neccesary for CDR copies, and
Duplication plants are unlikely to burn CD's of your record collection
for mass distribution.

But - could dither make the artifacts down at the bottom of a 16
bit file less irritating? Correct me if I'm wrong, but doesn't dither
not actually remove truncation distortion, but just make the artifacts
less irritating by tricking the ear with broadband noise? Of course
there is no bit reduction truncation here, but there are still
probably artifacts.

Anyway I would think if the DAT machine didn't apply dither, record
noise is kinda loud and pretty broadband already.

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Scott Dorsey]

WillStG wrote:

But - could dither make the artifacts down at the bottom of a 16
bit file less irritating? Correct me if I'm wrong, but doesn't dither
not actually remove truncation distortion, but just make the artifacts
less irritating by tricking the ear with broadband noise? Of course
there is no bit reduction truncation here, but there are still
probably artifacts.

Here we go again... NO.

Dither actually removes truncation distortion if it's performed properly
along with the truncation.

If there is no truncation, there is no need for dither.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[WillStG]

On May 20, 8:07 am, (Scott Dorsey) wrote:
WillStG wrote:

But - could dither make the artifacts down at the bottom of a 16
bit file less irritating? Correct me if I'm wrong, but doesn't dither
not actually remove truncation distortion, but just make the artifacts
less irritating by tricking the ear with broadband noise? Of course
there is no bit reduction truncation here, but there are still
probably artifacts.

Here we go again... NO.

Dither actually removes truncation distortion if it's performed properly
along with the truncation.

If there is no truncation, there is no need for dither.
--scott

--
"C'est un Nagra. C'est suisse, et tres, tres precis."

Not looking to argue Scott. I certainly in practice, true to
orthodoxy only use dither when truncating. But how does dither
actually remove truncation distortion - is this mathematics? And why
would it not be useful in the case of quantization error as well? The
RAP faq doesn't exactly explain it.

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Scott Dorsey]

WillStG wrote:

Not looking to argue Scott. I certainly in practice, true to
orthodoxy only use dither when truncating. But how does dither
actually remove truncation distortion - is this mathematics? And why
would it not be useful in the case of quantization error as well? The
RAP faq doesn't exactly explain it.

It _is_ mathematics and what it does is basically make the quantization
error random. So you get linearity well below the noise floor, in exchange
for a little bit more noise.

I don't have a good intuitive explanation for it, but as I recall Bob Katz's
book on mastering does.
--scott


--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[WillStG]

On May 20, 10:18 am, (Scott Dorsey) wrote:
WillStG wrote:

Not looking to argue Scott. I certainly in practice, true to
orthodoxy only use dither when truncating. But how does dither
actually remove truncation distortion - is this mathematics? And why
would it not be useful in the case of quantization error as well? The
RAP faq doesn't exactly explain it.

It _is_ mathematics and what it does is basically make the quantization
error random. So you get linearity well below the noise floor, in exchange
for a little bit more noise.


Ok, but an ADC also produces quantizing errors when converting to
digital in the first place, no? So why would dither be effective on
quantizng errors in the one case but not the other? Are they apples to
oranges in terms of what kind of errors they actually are? Is the term
"quantization errors" a too broad and perhaps overly used term?

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Anahata]

On Wed, 20 May 2009 06:56:08 -0700, WillStG wrote:
But how does dither actually
remove truncation distortion - is this mathematics? And why would it not
be useful in the case of quantization error as well? The RAP faq
doesn't exactly explain it.

I'll have a go:

When quantizing from an analog signal, or when truncating from more to
fewer bits, the key in both processes is that there is useful information
in the signal below the level at which you are quantizing. That
information is incorporated in the dither process.

Suppose you have an actual signal that is somewhere between two digital
value n and n + 1. Without dither, that will simply be represented as
either n or n + 1. With dither, it will be represented as randomly either
n or n + 1, but more frequently one or the other in proportion to which
value the real input it closest to, so if you had an unchanging input and
averaged many dithered values they'd average out to the exact input value.

Mathematical analysis can show that this is equivalent to a precise
indication of the input (to a higher precision than implied by just the
number of bits), plus random noise.

--
Anahata
==//== 01638 720444
http://www.treewind.co.uk ==//== http://www.myspace.com/maryanahata

[Scott Dorsey]

WillStG wrote:
Ok, but an ADC also produces quantizing errors when converting to
digital in the first place, no?

Right, because there is always noise in digital circuits. So your ladder
that is supposed to trigger at a particular voltage doesn't always trigger
at precisely the right voltage. So you get noise.

So why would dither be effective on
quantizng errors in the one case but not the other? Are they apples to
oranges in terms of what kind of errors they actually are?

Dither doesn't remove quantizing errors, it just makes them more random.
This gives you better linearity, but it doesn't do anything about noise
issues. Since what you need is linearity, it's a huge benefit.

Is the term
"quantization errors" a too broad and perhaps overly used term?

It is a very broad term, yes.
--scott
--
"C'est un Nagra. C'est suisse, et tres, tres precis."

[Arny Krueger]

"WillStG" wrote in message


Ok, but an ADC also produces quantizing errors when
converting to digital in the first place, no?

Yes.

So why
would dither be effective on quantizng errors in the one
case but not the other?


Dither must be part of the quantization process to be effective. It can be
applied before or during the quantization process.

Are they apples to oranges in
terms of what kind of errors they actually are? Is the
term "quantization errors" a too broad and perhaps overly
used term?

Quantization is pretty much a unique, well-understood thing.

[WillStG]

On May 20, 11:43 am, (Scott Dorsey) wrote:
WillStG wrote:
Ok, but an ADC also produces quantizing errors when converting to
digital in the first place, no?

Right, because there is always noise in digital circuits. So your ladder
that is supposed to trigger at a particular voltage doesn't always trigger
at precisely the right voltage. So you get noise.

So dither _is_ useful during Analog to digital conversion?


So why would dither be effective on
quantizng errors in the one case but not the other? Are they apples to
oranges in terms of what kind of errors they actually are?

Dither doesn't remove quantizing errors, it just makes them more random.
This gives you better linearity, but it doesn't do anything about noise
issues. Since what you need is linearity, it's a huge benefit.

Ok. So you can apply dither when recording, because the analog
signal contains information that, after being randomized by dither
along with the noise, can still be perceived and measured because of
"averaging", and also during truncation, because there is also audio
information below the top 16 bits to represent in the randomizing
scheme?

But in an existing undithered file, the greater information that
could have been included due to the averaging effect dither provides
has already been lost, and in it's place bit toggling distortion has
already been recorded. And the noise of dither isn't just a mask for
distortion that exists, it prevents distortion by randomizing.

Is this a correct explanation? The averaging effects of dither is
explained in the RAP faq, but an overall explanation is not, so you
can't just say "read the FAQ". And around here most guys just get
grumpy when someone asks for a simple explanation...

Will Miho
NY TV/Audio Post/music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Chris Hornbeck]

On Wed, 20 May 2009 14:03:46 -0700 (PDT), WillStG
wrote:


Ok. So you can apply dither when recording, because the analog
signal contains information that, after being randomized by dither
along with the noise, can still be perceived and measured because of
"averaging", and also during truncation, because there is also audio
information below the top 16 bits to represent in the randomizing
scheme?

Is this a correct explanation? The averaging effects of dither is
explained in the RAP faq, but an overall explanation is not,

The effect of dither to a (bandlimited, sampled) signal is
to allow an (ideally) *perfect* reproduction, the output
(ideally) *exactly* like the original - plus a small noise,
the dither itself.

Our ability to possibly hear below the noise background is
from the same mechanism that allows us to possibly hear below
any noise background, hearing in frequency bands.


Much thanks, as always,
Chris Hornbeck

[Ben Bradley[_2_]]

Let me try...

Quantizing errors from A/D conversion are actually a distortion -
the digitized waveform has harmonically related signals not in the
original analog signal. Think of a low level sine wave that only makes
one step move in the A/D converter, and make the step at the sine
wave's zero crossing. The digital output is a square wave. If you add
noise, the place where the A/D converter sees the sine wave "cross
zero" is different at each (half) cycle, and is random around that
crossing. The output will still be one step going on and off, but the
timing will on average make up a sine wave.

Thus adding noise before the A/D conversion (or before a bit
reduction) decorrelates these distortion products. They're still part
of the signal, but they're scattered around at all frequencies as a
slightly added noise to the dither noise.

Tape head AC bias is an inexact and crude but useful analogy to
dither. Bias added during magnetic tape recording makes for playback
of a linear signal, but a recording made without bias has distortion
that cannot be fixed.

I've posted this article before, hope it helps:
http://www.national.com/an/AN/AN-804.pdf

[Chris Hornbeck]

On Wed, 20 May 2009 20:38:21 -0400, Ben Bradley
wrote:

Thus adding noise before the A/D conversion (or before a bit
reduction) decorrelates these distortion products. They're still part
of the signal, but they're scattered around at all frequencies as a
slightly added noise to the dither noise.

This is probably as good as an explanation gets. It includes
the idea that the rounding errors don't just magically disappear,
but are randomized (another word for noise), and the deeper
idea that the errors become part of the background noise,
which is harder to grasp (well, impossible in for my pea brain.
Fun to try, though).


Much thanks, as always,
Chris Hornbeck

[WillStG]

On May 20, 8:38 pm, Ben Bradley wrote:
Let me try...

Quantizing errors from A/D conversion are actually a distortion -
the digitized waveform has harmonically related signals not in the
original analog signal. Think of a low level sine wave that only makes
one step move in the A/D converter, and make the step at the sine
wave's zero crossing. The digital output is a square wave. If you add
noise, the place where the A/D converter sees the sine wave "cross
zero" is different at each (half) cycle, and is random around that
crossing. The output will still be one step going on and off, but the
timing will on average make up a sine wave.

Thus adding noise before the A/D conversion (or before a bit
reduction) decorrelates these distortion products. They're still part
of the signal, but they're scattered around at all frequencies as a
slightly added noise to the dither noise.

Tape head AC bias is an inexact and crude but useful analogy to
dither. Bias added during magnetic tape recording makes for playback
of a linear signal, but a recording made without bias has distortion
that cannot be fixed.

I've posted this article before, hope it helps:http://www.national.com/an/AN/AN-804.pdf

Thanks Ben, your explanation's pretty clear, without dither
quantization errors are outputted as square wave distortion during ADC
and bit reduction, with dither the errors are randomized enough to
prevent square wave output. Also this preserves enough of the
original signal to make it perceptable and measurable, even as the
signal disappears below the noise floor. What is unclear is why dither
is provided as an "option" at all. Do all ADC's, such as those in DAT
machines and CDR recorders, and digital mixer summing busses include
it as part of "normal"encoding? And if one's DAW software has global
dither options selected - as part of it's internal digital mixer - is
it still neccessary to add dither plugins during bit reducing
processing? Conversely if one doesn't have global dither selected in
one's DAW, will it dither anyway or will you have to use a plugin to
prevent distortion on your mix output? The Waves plugs offer several
dither options in their L1/L2/L3 Maximizer's, how redundant is that -
aren't most Waves plugins dithering their output anyway? And I have
read Apogee's explanation of UV22 a few times, but why they provide 2
levels of dither is unclear - why wouldn't one always use the least
amount of noise possible to prevent distortion?

g

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom
Waits

[Keith.]

"anahata" wrote in message
o.uk...
On Wed, 20 May 2009 06:56:08 -0700, WillStG wrote:
But how does dither actually
remove truncation distortion - is this mathematics? And why would it not
be useful in the case of quantization error as well? The RAP faq
doesn't exactly explain it.

I'll have a go:

When quantizing from an analog signal, or when truncating from more to
fewer bits, the key in both processes is that there is useful information
in the signal below the level at which you are quantizing. That
information is incorporated in the dither process.

Suppose you have an actual signal that is somewhere between two digital
value n and n + 1. Without dither, that will simply be represented as
either n or n + 1. With dither, it will be represented as randomly either
n or n + 1, but more frequently one or the other in proportion to which
value the real input it closest to, so if you had an unchanging input and
averaged many dithered values they'd average out to the exact input value.

Mathematical analysis can show that this is equivalent to a precise
indication of the input (to a higher precision than implied by just the
number of bits), plus random noise.

--
Anahata
==//== 01638 720444
http://www.treewind.co.uk ==//== http://www.myspace.com/maryanahata

I am still coming to grips with this so how does this sound :-
Dithering creates a digital value for a signal that would normally be below
the quantizing level i.e. the bit rate is too coarse to asign a value to
this low level but valuable signal.
Dithering asigns a value to this signal that is retained as the bit rate is
lowered for normal processing.

It was mentioned previously that the bias signal applied to tapes to
'excite' the particles is an analogue to this.
Perhaps a carrier wave of a broadcast signal is another and I know that the
ear produces its own emissions
http://www.mja.com.au/public/issues/...d/redhead.html
as otoacoustic emissions.
Perhaps nature has beaten us to the idea!

Keith.

[Arny Krueger]

"Chris Hornbeck" wrote in
message
On Wed, 20 May 2009 14:03:46 -0700 (PDT), WillStG
wrote:

Ok. So you can apply dither when recording, because
the analog signal contains information that, after being
randomized by dither along with the noise, can still be
perceived and measured because of "averaging", and also
during truncation, because there is also audio
information below the top 16 bits to represent in the
randomizing scheme?

Yes. The general rule is dither whenever quantizing or re-quantizing.

Is this a correct explanation? The averaging effects
of dither is explained in the RAP faq, but an overall
explanation is not,

It's not an averaging effect, it is a randomizing effect.

Quantization noise is not really a noise - it is more properly called a
nonlinear distortion. Quantization distortion is determined by the signal
being converted and the sample rate. So for example, if you quantize a
steady pure tone, the quantization distortion will manifest itself as one or
more additional steady pure tones. Since these tones created by the
quantization distortion are steady and pure, they are relatively easy to
hear.

The function of the dither follows the same pattern. Think of the dither
noise as being a collection of randomly-varying tones. Just like the signal,
the quantization distortion will be generated that is a different collection
of randomly-varying tones. Since the distoriton is randomly-varying and
complex, it is less noticable and generally less objectionable.



The effect of dither to a (bandlimited, sampled) signal is
to allow an (ideally) *perfect* reproduction, the output
(ideally) *exactly* like the original - plus a small
noise, the dither itself.

Not quite. While dither increases the noise floor when applied, it is also
transformed by the quantization process. So the added noise is not the same
as the dither, but instead the rise in background noise is a predictable,
transformed version of the dither.

Our ability to possibly hear below the noise background is
from the same mechanism that allows us to possibly hear
below any noise background, hearing in frequency bands.

You probably meant:

Our ability to possibly hear below the noise background due to the dither
is
from the same mechanism that allows us to possibly hear below any noise
background, hearing in frequency bands.

[Arny Krueger]

"Ben Bradley" wrote in message


Tape head AC bias is an inexact and crude but useful
analogy to dither. Bias added during magnetic tape
recording makes for playback of a linear signal, but a
recording made without bias has distortion that cannot be
fixed.

Good point. It turns out that if you replace dither with a very high
frequency tone, it will have many of the same benefits.

[WillStG]

On May 21, 6:40 am, "Arny Krueger" wrote:
"Chris Hornbeck" wrote in
messagenews:60t815t047rqisd5r85il98d4fllruk1q1@4ax .com

On Wed, 20 May 2009 14:03:46 -0700 (PDT), WillStG
wrote:
Ok. So you can apply dither when recording, because
the analog signal contains information that, after being
randomized by dither along with the noise, can still be
perceived and measured because of "averaging", and also
during truncation, because there is also audio
information below the top 16 bits to represent in the
randomizing scheme?

Yes. The general rule is dither whenever quantizing or re-quantizing.

Is this a correct explanation? The averaging effects
of dither is explained in the RAP faq, but an overall
explanation is not,

It's not an averaging effect, it is a randomizing effect.

heh heh - read the FAQ Arny....

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Arny Krueger]

"WillStG" wrote in message

On May 21, 6:40 am, "Arny Krueger"
wrote:
"Chris Hornbeck" wrote
in messagenews:60t815t047rqisd5r85il98d4fllruk1q1@4ax .com

On Wed, 20 May 2009 14:03:46 -0700 (PDT), WillStG
wrote:
Ok. So you can apply dither when recording, because
the analog signal contains information that, after
being randomized by dither along with the noise, can
still be perceived and measured because of
"averaging", and also during truncation, because there
is also audio information below the top 16 bits to
represent in the randomizing scheme?

Yes. The general rule is dither whenever quantizing or
re-quantizing.

Is this a correct explanation? The averaging effects
of dither is explained in the RAP faq, but an overall
explanation is not,

It's not an averaging effect, it is a randomizing effect.

heh heh - read the FAQ Arny....

Been there, done that.

Here's where it talks about dithering and averaging:

"However, if we look at (or listen to) much more than a single
sample, through the process of averaging, both instruments and
the ear are capable of detecting real signals below the noise
floor. Let's look at the simple case of a constant voltage that
is 1/10th the value of the noise floor. At the instantaneous or
sample point, the noise value overwhelms the signal completely.
But, as we collect more consecutive snapshots or samples, an
interesting thing begins to happen. The noise (or dither) is
random and its long-term average is, in fact, 0. But the signal
has a definite value, 1/10. Average the signal long enough, and
the average value due to the noise approaches 0, but the average
value of the signal remains constant at 1/10."

Note that the averaging that is mentioned here is done by the human ear, not
the dithering.

The human ear averages, not the dither. It's an important distinction.
Dither doesn't have an averaging effect on the signal. It exploits the
averaging that is done by the human ear.

[WillStG]

On May 21, 8:16 am, "Arny Krueger" wrote:
"WillStG" wrote in message





On May 21, 6:40 am, "Arny Krueger"
wrote:
"Chris Hornbeck" wrote
in messagenews:60t815t047rqisd5r85il98d4fllruk1q1@4ax .com

On Wed, 20 May 2009 14:03:46 -0700 (PDT), WillStG
wrote:
Ok. So you can apply dither when recording, because
the analog signal contains information that, after
being randomized by dither along with the noise, can
still be perceived and measured because of
"averaging", and also during truncation, because there
is also audio information below the top 16 bits to
represent in the randomizing scheme?

Yes. The general rule is dither whenever quantizing or
re-quantizing.
Is this a correct explanation? The averaging effects
of dither is explained in the RAP faq, but an overall
explanation is not,
It's not an averaging effect, it is a randomizing effect.
heh heh - read the FAQ Arny....

Been there, done that.

Here's where it talks about dithering and averaging:

"However, if we look at (or listen to) much more than a single
sample, through the process of averaging, both instruments and
the ear are capable of detecting real signals below the noise
floor. Let's look at the simple case of a constant voltage that
is 1/10th the value of the noise floor. At the instantaneous or
sample point, the noise value overwhelms the signal completely.
But, as we collect more consecutive snapshots or samples, an
interesting thing begins to happen. The noise (or dither) is
random and its long-term average is, in fact, 0. But the signal
has a definite value, 1/10. Average the signal long enough, and
the average value due to the noise approaches 0, but the average
value of the signal remains constant at 1/10."

Note that the averaging that is mentioned here is done by the human ear, not
the dithering.

The human ear averages, not the dither. It's an important distinction.
Dither doesn't have an averaging effect on the signal. It exploits the
averaging that is done by the human ear.

Well don't leave people with the impression that it's a
psychoacoustic trick of the human ear. Averaging also makes the
dithered signal measurable, it's not just the ear that can perceive
the infromation that "averaging" preserves.

Will Miho
NY TV/Audio Post/Music/Live Sound Guy
"The large print giveth and the small print taketh away..." Tom Waits

[Chris Hornbeck]

On Thu, 21 May 2009 06:40:22 -0400, "Arny Krueger"
wrote:

The effect of dither to a (bandlimited, sampled) signal is
to allow an (ideally) *perfect* reproduction, the output
(ideally) *exactly* like the original - plus a small
noise, the dither itself.

Not quite. While dither increases the noise floor when applied, it is also
transformed by the quantization process. So the added noise is not the same
as the dither, but instead the rise in background noise is a predictable,
transformed version of the dither.

And to be really complete, we'll also have to include the
(otherwise mysteriously missing) quantization errors in the
background noise. They and the dither "signal" get mashed
up together and spread across time in ways of which Doctor McCoy
would have never approved. ("He's dead, Jim.")

You probably meant:

Our ability to possibly hear below the noise background due
to the dither is from the same mechanism that allows us to
possibly hear below any noise background, hearing in frequency bands.

Much cleaner, thanks.

Others can have differing opinions (they're simply WRONG, but
that's free will...) but for me, there's no cooler idea in any
technical field than dither. It's snot slick and deeper than
whale ****.


Much thanks, as always,
Chris Hornbeck